How to transform (translate, rotate, scale) Vertex Groups using drivers?
The simplest way to move a vertex group is using an armature: create a single bone armature, give to the bone the exact name of the vertex group, add an armature modifier to the mesh and select the newly created armature in the modifier's object field.

Now if you move, rotate and scale the bone (even with drivers) the vertex group will exactly follow.

You can have as many bones (and associated vertex groups) as you want in the armature, but - if you want rigid movements - make sure that every single vertex is affected by one bone-vertexgroup only.